Nest on Ice Air 8RSXC18 heat pump PTAC: R reads DC, not 24VAC. Relays + separate transformer?

Renter here. I'm trying to swap the Riseem thermostat on my Ice Air PTAC for a Nest (4th gen) and ran into a power issue. I saw the older thread here about a Nest on an Ice Air PTAC, but my situation looks a bit different. Pics attached: my before/after wiring diagram, the unit's wiring label, the board, and the thermostat wiring.

Unit info: Ice Air 8RSXC18 heat pump, chassis ELA-13347, logic V3.3_20230817. The control label says WG7010010001400 and the main board is Wellgo WG3220010004100.

What's going on:
The wiring label says R is 24VAC, but when I measure R to C I get 20+ V on DC, around 6 V on AC, and about 0 Hz. Same reading at the board and at the thermostat. The Nest shows "No power" even with C hooked up.

The Riseem works fine because it runs on batteries/power stealing and doesn't need C. It's basically just a switch connecting R to Y, W, etc. If I jump R to Y or R to W at the thermostat wires, the unit runs, fan and all.

From what I can find, Ice Air's own factory Nest option lists a "12V DC control signal," so I'm guessing DC on R is normal for this unit and not a fault.

What I want to do:

• Plug-in 24VAC transformer to power the Nest by itself
• The Nest's Y, W and G outputs each drive a relay (Functional Devices RIBU1C)
• Each relay just connects the board's own R to Y, W or F3, the same thing the Riseem does now
• The transformer side and the PTAC side never touch. Board C stays disconnected

Question:
Would this work, and is there anything I'm missing or should watch out for? I'm also a little unsure whether the relay contacts will switch reliably at whatever tiny current these inputs draw.

Thanks in advance!